A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$6.00$, and bags of cookies cost $$4.50$, and sales equaled $$58.50$ in total. There were $6$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6x+4.5y = 58.5}$ ${y = x+6}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+6}$ for $y$ in the first equation. ${6x + 4.5}{(x+6)}{= 58.5}$ Simplify and solve for $x$ $ 6x+4.5x + 27 = 58.5 $ $ 10.5x+27 = 58.5 $ $ 10.5x = 31.5 $ $ x = \dfrac{31.5}{10.5} $ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $ {y = x+6}$ to find $y$ ${y = }{(3)}{ + 6}$ ${y = 9}$ You can also plug ${x = 3}$ into $ {6x+4.5y = 58.5}$ and get the same answer for $y$ ${6}{(3)}{ + 4.5y = 58.5}$ ${y = 9}$ $3$ bags of candy and $9$ bags of cookies were sold.